SCHDM2017 @ YITP Theoretical study of

SCHDM2017 @ YITP

Theoretical study of Λ(1405) in Ξb decay

Kenta Miyahara (Kyoto univ.)Tetsuo Hyodo (YITP)Eulogio Oset (Valencia univ.)

1

25 May 2017

Contents❖ Introduction

- Λ(1405) previous exp.

- recent heavy hadron exp.

❖ Formulation

- weak decay, qq creation, FSI

❖ Results ( with chiral unitary approach )

- dip structure ← Λ(1405) peak

❖ Other reactions

❖ Summary

2

❖ Λ(1405) : I (JP) = 0 (1/2-), S=-1• “exotic” candidate

sd

uΛ* =KN

!Σ

and/or

• puzzle : pole structureHyodo and Jido, Prog. Part. Nucl. Phys. 67, 55 (2012)

3

Introduction : Λ(1405)

Λ(1405) is an interesting but mysterious state.

Λ(1405) peak in spectrum resonance pole

single pole double pole or

doorway to K nuclei S. Ohnishi, et al., arXiv:1701.07589

4

Introduction : Λ(1405) previous exp.

TπΣ→πΣ has not been measured.

• γp→K+(πΣ)

• K-p→π0(πΣ)

Magas, Oset, and Ramos, Phys. Rev. Lett. 95 (2005) 052301

exp.) LEPS : Niiyama et al., Phys. Rev. C78 (2008) 035202CLAS : Moriya et al., Phys. Rev. C87 (2013) 035206

Roca and Oset, Phys. Rev. C87 (2013) 055201

exp.) Crystal Ball : Prakhov et al., Phys. Rev. C70 (2004) 034605

is dominant

d�

dMinv/ |b(W )G⇡⌃T⇡⌃!⇡⌃ + c(W )GKNTKN!⇡⌃|2

TKN!⇡⌃

5

Introduction : heavy hadron decays

We search for decays dominated by TπΣ→πΣ.

• Λb → J/ψ K-p decayAaij et al., Phys. Rev. Lett. 115 (2015) 072001

Pc(4450)

Pc(4380)

pentaquarks

in J/ψ p spectrum

• Λc+ → π+ (πΣ) decay Λ(1405)Miyahara, Hyodo, and Oset, Phys. Rev. C92 (2015) 055204

Λ(1405)in πΣ spectrum

TKN→πΣ is dominant

theoreticalprediction

Formulation

6

Considering Cabibbo-Kobayashi-Maskawa matrix, kinematics, and diquark correlation, the following diagram is favored.

Weak decay creationqq

M

B

Final state interaction

⇤(1405)

I(JP ) = 0(1/2�)

uu+ dd+ ss

su

⌅0b

b

uJP = 1

2

+

cD0

W�

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Formulation : Weak decay

❖ Cabibbo favored diagrams

su

⌅0b

b

u

JP = 12

+

cD0

W�

d

su

⇤⇤

(a)

su

buc

D0

W�

⇤⇤

su

u

du

(b)

8


su

⌅0b

b

u

JP = 12

+

cD0

W�

d

su

⇤⇤

(a)

su

buc

D0

W�

⇤⇤

su

u

du

(b)

high momentum

soft qq creation


9



su

⌅0b

b

u

JP = 12

+

cD0

W�

d

su

⇤⇤

(a)

su

buc

D0

W�

⇤⇤

su

u

du

(b)

Diagram (a) is most favored.

for momentummismatch

10

Formulation : qq creation

❖ quark d.o.f. → hadron d.o.f.

⌅0b

b

u

JP = 12

+c

D0

W�

d

su

su

spectatorS = 0

even parity

parity odd(L = 1)

Λ(1405)parity odd

|⌅0bi = 1p

2|b(su� us)i

1p2|d(su� us)i

weak decay

11



|⌅0bi = 1p

2|b(su� us)i

1p2

X

i=u,d,s

|dqiqi(su� us)iqq creation

1p2|d(su� us)i

weak decay

M 0 B0

⌅0b

b

u

JP = 12

+c

D0

W�

d

su

su

qq

spectatorS = 0

even parity

parity odd(L = 1)

M 0

B0

12



|⌅0bi = 1p

2|b(su� us)i

1p2|d(su� us)i

weak decay

⌅0b

b

u

JP = 12

+c

D0

W�

d

su

su

qq

spectatorS = 0

(even parity)

parity odd(L = 1)

M 0

B0

1p2

X

i=u,d,s


M 0 B0M =

0

@uu ud usdu dd dssu sd ss

1

A =

0

BB@

⇡0p2+ ⌘p

3+ ⌘0

p6

⇡+ K+

⇡� � ⇡0p2+ ⌘p

3+ ⌘0

p6

K0

K� K0 � ⌘p3+ 2⌘0

p6

1

CCA

considering SU(3) transformation,

used in Chiral EFT

B =1p2

0

@u(ds� sd) u(su� us) u(ud� du)d(ds� sd) d(su� us) d(ud� du)s(ds� sd) s(su� us) s(ud� du)

1

A =

0

B@

⌃0p2+ ⇤p

6+ ⇤1p

3⌃+ p

⌃� �⌃0p2+ ⇤p

6+ ⇤1p

3n

⌅� ⌅0 � 2p6⇤+ ⇤1p

3

1

CA

q : 3 → 3 diquark

13



|⌅0bi = 1p

2|b(su� us)i

1p2|d(su� us)i

weak decay

⌅0b

b

u

JP = 12

+c

D0

W�

d

su

su

qq

spectatorS = 0

(even parity)

parity odd(L = 1)

M 0

B0

1p2

X

i=u,d,s


M 0 B0M =

0

@uu ud usdu dd dssu sd ss

1

A =

0

BB@

⇡0p2+ ⌘p

3+ ⌘0

p6

⇡+ K+

⇡� � ⇡0p2+ ⌘p

3+ ⌘0

p6

K0

K� K0 � ⌘p3+ 2⌘0

p6

1

CCA

considering SU(3) transformation,

used in Chiral EFT

B =1p2

0

@u(ds� sd) u(su� us) u(ud� du)d(ds� sd) d(su� us) d(ud� du)s(ds� sd) s(su� us) s(ud� du)

1

A =

0

B@

⌃0p2+ ⇤p

6+ ⇤1p

3⌃+ p

⌃� �⌃0p2+ ⇤p

6+ ⇤1p

3n

⌅� ⌅0 � 2p6⇤+ ⇤1p

3

1

CA

q : 3 → 3 diquark

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|⌅0bi = 1p

2|b(su� us)i

1p2

X

i=u,d,s


1p2|d(su� us)i

weak decay

M 0 B0

⌅0b

b

u

JP = 12

+c

D0

W�

d

su

su

qq

spectatorS = 0

even parity

parity odd(L = 1)

M 0

B0

|MB0i = � 1

2p3|⇡0⇤i+ 1

2|⇡0⌃0i+ |⇡�⌃+i+ 1

3p2|⌘⇤i � 1p

6|⌘⌃0i+ |K0⌅0i

15



|⌅0bi = 1p

2|b(su� us)i

1p2

X

i=u,d,s


1p2|d(su� us)i

weak decay

M 0 B0

⌅0b

b

u

JP = 12

+c

D0

W�

d

su

su

qq

spectatorS = 0

(even parity)

parity odd(L = 1)

M 0

B0

no KN state !!TπΣ→πΣ is dominant

|MB0i = � 1

2p3|⇡0⇤i+ 1

2|⇡0⌃0i+ |⇡�⌃+i+ 1

3p2|⌘⇤i � 1p

6|⌘⌃0i+ |K0⌅0i

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Formulation : Final State Interaction

Gi : meson-baryon loop function, Tij : meson-baryon scattering matrix

coefficients can be determined from |MB’>

u

d

s

b

⇡+Mj

Bj

Mj

Bj

T

Mj

Bj

hj

= +

G

VPVP

hj

d�j

dMinv=

1

(2⇡)3pD0 pjM⌅0

bMj

M2⌅0

b

|Mj |2

h⇡0⇤0 = � 1

2p3,

h⇡0⌃0 =1

2, h⇡�⌃+ = 1, h⇡+⌃� = 0,

hK�p = hK0n = 0,

h⌘⇤ =1

3p2, h⌘⌃0 = 0, hK0⌅0 = 1, hK+⌅� = 0

decay spectrum two-body amplitude T

Mj = VP

hj +

X

i

hiGi(Minv)Tij(Minv)

!

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Results : chiral unitary approach

T V V T

G

+=

T = V + V GT = V + V GV + V GV GV + · · ·= (V �1 �G)�1

Chiral EFT

❖ model for two-body T matrix

IHW model. Ikeda, Hyodo and Weise, Nucl. Phys. A881, 98 (2012)

• fit near the KN threshold including new exp. data• s-wave meson-baryon scattering with NLO term• with isospin breaking

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Results : invariant mass distribution

0

0.004

0.008

0.012

1320 1340 1360 1380 1400 1420 1440 1460

dΓ

j/dM

inv

[arb

. units

]

Minv [MeV]

π0Σ0

π-Σ+π+Σ-

⌅0b ! D0(⇡⌃)

19


0

0.004

0.008

0.012

1320 1340 1360 1380 1400 1420 1440 1460

dΓ

j/dM

inv

[arb

. units

]

Minv [MeV]

π0Σ0

π-Σ+π+Σ-

⌅0b ! D0(⇡⌃)

Λ(1405) peak ?

• different “Λ(1405) peak” positions ?

• quite low positions (π-Σ+ & π0Σ0) ?

20


0

0.004

0.008

0.012

1320 1340 1360 1380 1400 1420 1440 1460

dΓ

j/dM

inv

[arb

. units

]

Minv [MeV]

π0Σ0π-Σ+

π+Σ-

⌅0b ! D0(⇡⌃)

0

0.01

0.02

0.03

0.04

0.05

1320 1340 1360 1380 1400 1420 1440 1460

IHW

| T

πΣ

->

πΣ |

Minv [MeV]

| Tπ

-Σ

+ -> π0Σ

0 | | T

π-Σ

+ -> π-Σ

+ | | T

π-Σ

+ -> π+Σ

- |

two-body T

• I=1 interference

|⇡0⌃0i ⇠ � 1p3|⇡⌃iI=0

|⇡�⌃+i ⇠ � 1p3|⇡⌃iI=0 � 1p

2|⇡⌃iI=1

|⇡+⌃�i ⇠ � 1p3|⇡⌃iI=0 + 1p

2|⇡⌃iI=1

difference in Ξb0 is much larger

peak difference

small peak difference in T

Λ(1405) in TπΣ→πΣ can be extracted from Ξb0 decay.21


0

0.004

0.008

0.012

1320 1340 1360 1380 1400 1420 1440 1460

dΓ

j/dM

inv

[arb

. units

]

Minv [MeV]

π0Σ0π-Σ+

π+Σ-

⌅0b ! D0(⇡⌃)

0

0.01

0.02

0.03

0.04

0.05

1320 1340 1360 1380 1400 1420 1440 1460

IHW

| T

πΣ

->

πΣ |

Minv [MeV]

| Tπ

-Σ

+ -> π0Σ

0 | | T

π-Σ

+ -> π-Σ

+ | | T

π-Σ

+ -> π+Σ

- |

two-body T

Λ(1405)“dips” in π0Σ0 and π-Σ+ correspond to Λ(1405) in T.

Mj = VP

hj +

X

i

hiGi(Minv)Tij(Minv)

!

• “dip” origin

T

Mj

Bj

hj

= +

Ghj

interference between “tree” and “rescattering”

hj=0 in π+Σ-dip appearspeak

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Results : “peak” v.s. “dip” against KN fraction“dip” is characteristic of TπΣ→πΣ dominated reaction

existing TKN→πΣ dominated reactions reveal “peak”

x (|K�pi+ |K0

ni)

|MB0i = � 1

2p3|⇡0⇤i+ 1

2|⇡0⌃0i+ |⇡�⌃+i

+1

3p2|⌘⇤i � 1p

6|⌘⌃0i+ |K0⌅0i

When x < 0.5, “dip” would appear.

0

0.004

0.008

0.012

1320 1340 1360 1380 1400 1420 1440 1460

Ξb0 -> D0(πΣ)

dΓ

j/dM

inv

[arb

. u

nits

]

Minv [MeV]

x=0

x=0.2

x=0.4

x=0.6Ξb0→D0(π0Σ0)

strong coupling to Λ(1405)

weaker coupling to Λ(1405)

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Results : “peak” v.s. “dip” against KN fraction“dip” is characteristic of TπΣ→πΣ dominated reaction

weaker coupling to Λ(1405)

existing TKN→πΣ dominated reactions reveal “peak”strong coupling to Λ(1405)

x (|K�pi+ |K0

ni)

|MB0i = � 1

2p3|⇡0⇤i+ 1

2|⇡0⌃0i+ |⇡�⌃+i

+1

3p2|⌘⇤i � 1p

6|⌘⌃0i+ |K0⌅0i

0

0.004

0.008

0.012

1320 1340 1360 1380 1400 1420 1440 1460

Ξb0 -> D0(πΣ)

dΓ

j/dM

inv

[arb

. u

nits

]

Minv [MeV]

x=0

x=0.2

x=0.4

x=0.6Ξb0→D0(π0Σ0)

“dip”　　　 “fake peak”

When x < 0.5, “dip” would appear.

We have to note whether the peak is

“real” or “fake”.

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Other diagrams❖ reactions dominated by TπΣ→πΣ

Ξc+→νll+(πΣ)

suc d

l+

⌫M 0

B0

Ξc+→π+(πΣ)

suc d

M 0

B0

ud ⇡+

Ξc0→K0(πΣ)

s

cM 0

B0

d

u

d

sK0

○ only one diagram○ no contribution from

other hadron interactions× neutrino cannot be

measured

× many other diagrams× π+M, π+B interaction

may contribute in some channels

○ all final state can be caught

× many other diagrams× K0M, K0B interaction may

contribute in some channels

○ all final state can be caught

○ Cabibbo favored

Summary❖ We have studied the Ξb0→D0(πΣ) decay.

❖ Respecting the SU(3) sym., we have connected the quark d.o.f. and hadron d.o.f.

❖ From the CKM matrix and kinematics, it turns out that the Ξb0 decay is dominated by TπΣ→πΣ.

❖ Λ(1405) signal is seen as a peak in π+Σ-, and a “dip” in π0Σ0 and π-Σ+ due to the interference between tree and rescattering diagrams.

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“fake peak” may appear when the KN fraction is small.

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